1.
One-to-one function
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In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness, it never maps distinct elements of its domain to the same element of its codomain. In other words, every element of the codomain is the image of at most one element of its domain. The term one-to-one function must not be confused with one-to-one correspondence, occasionally, an injective function from X to Y is denoted f, X ↣ Y, using an arrow with a barbed tail. A function f that is not injective is sometimes called many-to-one, however, the injective terminology is also sometimes used to mean single-valued, i. e. each argument is mapped to at most one value. A monomorphism is a generalization of a function in category theory. Let f be a function whose domain is a set X, the function f is said to be injective provided that for all a and b in X, whenever f = f, then a = b, that is, f = f implies a = b. Equivalently, if a ≠ b, then f ≠ f, in particular the identity function X → X is always injective. If the domain X = ∅ or X has only one element, the function f, R → R defined by f = 2x +1 is injective. The function g, R → R defined by g = x2 is not injective, however, if g is redefined so that its domain is the non-negative real numbers [0, +∞), then g is injective. The exponential function exp, R → R defined by exp = ex is injective, the natural logarithm function ln, → R defined by x ↦ ln x is injective. The function g, R → R defined by g = xn − x is not injective, since, for example, g = g =0. More generally, when X and Y are both the real line R, then a function f, R → R is one whose graph is never intersected by any horizontal line more than once. This principle is referred to as the line test. Functions with left inverses are always injections and that is, given f, X → Y, if there is a function g, Y → X such that, for every x ∈ X g = x then f is injective. In this case, g is called a retraction of f, conversely, f is called a section of g. Conversely, every injection f with non-empty domain has an inverse g. Note that g may not be an inverse of f because the composition in the other order, f o g. In other words, a function that can be undone or reversed, injections are reversible but not always invertible

2.
One-to-one correspondence
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In mathematical terms, a bijective function f, X → Y is a one-to-one and onto mapping of a set X to a set Y. A bijection from the set X to the set Y has a function from Y to X. If X and Y are finite sets, then the existence of a means they have the same number of elements. For infinite sets the picture is complicated, leading to the concept of cardinal number. A bijective function from a set to itself is called a permutation. Bijective functions are essential to many areas of including the definitions of isomorphism, homeomorphism, diffeomorphism, permutation group. Satisfying properties and means that a bijection is a function with domain X and it is more common to see properties and written as a single statement, Every element of X is paired with exactly one element of Y. Functions which satisfy property are said to be onto Y and are called surjections, Functions which satisfy property are said to be one-to-one functions and are called injections. With this terminology, a bijection is a function which is both a surjection and an injection, or using words, a bijection is a function which is both one-to-one and onto. Consider the batting line-up of a baseball or cricket team, the set X will be the players on the team and the set Y will be the positions in the batting order The pairing is given by which player is in what position in this order. Property is satisfied since each player is somewhere in the list, property is satisfied since no player bats in two positions in the order. Property says that for each position in the order, there is some player batting in that position, in a classroom there are a certain number of seats. A bunch of students enter the room and the instructor asks them all to be seated. After a quick look around the room, the instructor declares that there is a bijection between the set of students and the set of seats, where each student is paired with the seat they are sitting in. The instructor was able to conclude there were just as many seats as there were students. For any set X, the identity function 1X, X → X, the function f, R → R, f = 2x +1 is bijective, since for each y there is a unique x = /2 such that f = y. In more generality, any linear function over the reals, f, R → R, f = ax + b is a bijection, each real number y is obtained from the real number x = /a. The function f, R →, given by f = arctan is bijective since each real x is paired with exactly one angle y in the interval so that tan = x

3.
One to One (Howard Jones album)
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One to One is the third album by British pop musician Howard Jones, released in October 1986. The CD release also contains the version of No One Is to Blame with Phil Collins on backing vocals. The album contained the hits You Know I Love You. Dont You. the album reached number 10 in the UK and was certified Gold for shipments in excess of 100,000 copies. −4,05 The Balance of Love −4,29 All I Want −4,37 Where Are We Going, −5,01 Dont Want to Fight Anymore −4,37 Step Into These Shoes −4,19 Will You Still Be There. Track #11 Produced by Phil Collins & Hugh Padgham Engineered by Hugh Padgham, additional credits Cover photo, Chris Garnham Inside photos, Simon Fowler

4.
One to One (Syreeta album)
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One To One is the third studio album released by Motown recording artist Syreeta Wright in 1977. It was the first album Wright released where former husband Stevie Wonder did not oversee most of its production, by the time of its release, Wright was a noted yet overlooked artist on the Motown label. In 1975, Wright and Wonder wrote and produced a love song titled Harmour Love. Because Wonder was busy working on his own project, Songs in the Key of Life. Rapper Currensys hip-hop group, Jet Life, takes a sample of I Too Am Waiting in their song 1st Place, upon her return, Wright began to wear braids and was emotionally inspired by her three-week stay. Wright and Robertson wrote most of the songs with Ware arranging the music, Wright also sung her own background vocals with the only other vocal assistances being longtime Motown background vocalist Jim Gilstrap and Ware himself. Wares productions were noted for its sensuality and he touched on some of the songs with Wright, the only song Wright didnt compose was the African-inspired Tiki Tiki Donga, which was written by Robertson and Ware, with Wright reaching high notes in her vibrato. Other songs, such as the track, Rest Yourself. Ware co-wrote music for the sexy ballad I Too Am Waiting and Ware, the sole Wonder production, Harmour Love, was included in the last minute. Wright was reassigned before the release to Tamla Records, which overlook many of her former husbands music. The album was released on February 9,1977, Wright produced a video for the song which featured the singer performing the song in a recording studio. The album was critically well-received upon its release, later that year, Wright focused on duet work with singer G. C. Cameron on the album, Rich Love, Poor Love, One to One I Dont Know Rest Yourself I Too Am Waiting Tiki Tiki Donga Dont Cry Harmour Love One to One Produced by Leon Ware, Syreeta Wright, Stevie Wonder and Curtis Robertson Jr

5.
Ed Bruce
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William Edwin Ed Bruce, Jr. is an American country music songwriter and singer. He is known for penning the 1975 song Mammas Dont Let Your Babies Grow Up to Be Cowboys and he also co-starred in the television series Bret Maverick with James Garner during the 1981-82 season. Bruce was born in Keiser, Arkansas and grew up in Memphis, in 1957, at the age of 17, he went to see Jack Clement, a recording engineer for Sun Records. Bruce caught the attention of Sun owner Sam Phillips, for whom he wrote and recorded Rock Boppin Baby. In 1962, he wrote Save Your Kisses for pop star Tommy Roe, charlie Louvin recorded See the Big Man Cry in 1965, Louvins version reached No.7 on the Billboard Country Singles chart. In the early 1960s, Bruce recorded for RCA and some smaller labels like Wand/Scepter, singing rockabilly music, however, he didnt achieve significant success as a vocalist during this period. In 1966, he returned to RCA and recorded Puzzles, The Price I Pay to Stay and he still did not achieve great charting action. He made money doing voice-overs for television and radio commercials and he scored his first charted single with Walkers Woods in 1967, and also charted with his version of The Monkees Last Train to Clarksville. Both of these singles were minor hits, in 1969, Bruce signed with Monument Records, where he continued to have minor successes with Everybody Wants To Go To Heaven and Song For Jenny. Meanwhile, he continued to write songs like The Man That Turned My Mama On and he signed with United Artists Records in 1973 and released several singles, but only one single in 1974 became a minor hit. He finally made the regions of the charts when he made the Top 20 on the country charts with his version of Mamas Dont Let Your Babies Grow Up to Be Cowboys in 1976. In 1978, Mamas Dont Let Your Babies Grow up to Be Cowboys was recorded by Willie Nelson and Waylon Jennings and it became a major hit, and put Bruce on an upward swing. Two more Top 40 hits followed for Bruce in 1976, and in 1977, in 1979, Tanya Tucker took Bruces song Texas into the country Top 5. In 1980, Bruce signed with MCA Records, where he would score his biggest successes and his early hits with MCA included Diane, The Last Cowboy Song, When You Fall In Love, Evil Angel, and Loves Found You And Me. His biggest hit, Youre the Best Break This Old Heart Ever Had went to one on the country chart in 1982. This also was Bruces first Top 10 as a singer after 15 years and he had other hit songs that made the Top 10 like Ever, Never Lovin You, My First Taste of Texas, and After All. In 1984, he returned to RCA Records and scored a No.3 hit with You Turn Me On Like A Radio in 1985 and his last Top 10 single was Nights in 1986 and his last Top 40 single was Quietly Crazy in 1987. During this time, Bruce began to act and do commercials, one of his biggest acting roles was as the second lead on the television revival of 1957s Maverick, called Bret Maverick

6.
One to One (TV series)
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One to One is an Irish television series which airs on RTÉ One. Since the first edition was broadcast at 12, 15pm on 1 October 2006, the second series moved to a Monday slot, beginning on 1 October 2007. A third series was broadcast during the months of June. The fourth series commenced airing on 10 November 2008, series presenters have included Aine Lawlor, Bryan Dobson, George Lee, Richard Crowley, Paul Cunningham, John Murray and Cathal Mac Coille. Each edition is approximately forty minutes length in total, with all the interviews available to watch online at RTÉ. ie. The first episode featured an interview by Lawlor with Diarmuid Martin, the second episode featured an interview by Crowley with Nickey Brennan, the President of the Gaelic Athletic Association. The third episode featured an interview by Dobson with Ombudsman and Information Commissioner Emily OReilly and she spoke of her pity for those she viewed as the marginalised members of society, directing her frustration at Irelands Health Service Executive for not dealing with such complaints appropriately. The fifth episode featured an interview by Lawlor with the Director of the Economic and Social Research Institute, the sixth episode featured an interview by Dobson with the consultant cardiac surgeon, Maurice Neligan. He also criticised a proposal to close hospitals in Ennis, Monaghan, Nenagh, the seventh episode featured an interview by Lee with the billionaire businessman, Michael Smurfit. This discrimination, he said, served as motivation for Smurfit to expand his business into a worldwide organisation with annual profits of €7 billion which employs 40,000 people. The eighth episode featured an interview by Lawlor with the Artistic Director of the Gate Theatre in Dublin and he spoke of first meeting his hero, the playwright Samuel Beckett in Paris in 1986. Colgan and Alan Moloney, his business partner, eventually committed all nineteen of Becketts plays onto film in 2001 in a joint project for RTÉ, Channel 4, the ninth episode featured an interview by Crowley with Ben Dunne, businessman. The tenth episode featured an interview by Dobson with the Director of the charity Trócaire and he spoke of the 2004 Asian tsunami, Ethiopia and the continent of Africa, airing his belief that it has gone backwards within the space of two decades. Kilculln also spoke of the agencys Catholic ethos and how this presents difficulty when it comes to working against HIV/Aids, the eleventh episode features an interview by Crowley with Theo Dorgan, a poet, broadcaster and member of the Arts Council of Ireland. The twelfth episode featured an interview by Lee with former Attorney General and European Commissioner and current Financial Adviser to the Vatican, Peter Sutherland. The first episode of the series featured an interview by Crowley with P. J. Mara. The second episode featured an interview by Dobson with former Minister of State and Deputy Leader of the Progressive Democrats, the third episode featured an interview by Lawlor with Jack OConnor, the General President of the SIPTU trade union. The fourth episode featured an interview by Crowley with Ulick McEvaddy, the fifth episode featured an interview by Dobson with the economic architect of Ireland, T. K. Whitaker

7.
Point-to-point (telecommunications)
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In telecommunications, a point-to-point connection refers to a communications connection between two nodes or endpoints. An example is a call, in which one telephone is connected with one other. This is contrasted with a point-to-multipoint or broadcast connection, in which many nodes can receive information transmitted by one node, other examples of point-to-point communications links are leased lines, microwave relay links, and two way radio. Point-to-point is sometimes abbreviated as P2P and this usage of P2P is distinct from P2P referring to peer-to-peer for file sharing networks. A traditional point-to-point data link is a medium with exactly two endpoints and no data or packet formatting. The host computers at either end had to take responsibility for formatting the data transmitted between them. The connection between the computer and the medium was generally implemented through an RS-232 or similar interface. Computers in close proximity may be connected by wires directly between their interface cards, when connected at a distance, each endpoint would be fitted with a modem to convert analog telecommunications signals into a digital data stream. When the connection used a telecommunications provider, the connections were called a dedicated, leased, the ARPANET used leased lines to provide point-to-point data links between its packet-switching nodes, which were called Interface Message Processors. In, the term point-to-point telecommunications relates to fixed wireless communications for Internet or voice over IP via radio frequencies in the multi-gigahertz range. The Telecommunications Industry Associations engineering committees develop U. S. standards for point-to-point communications, online tools help users find if they have such line of sight. The telecommunications signal is typically bi-directional, either time division multiple access or channelized, in hubs and switches, a hub provides a point-to-multipoint circuit which divides the total bandwidth supplied by the hub among each connected client node. Within many switched telecommunications systems, it is possible to establish a permanent circuit, one example might be a telephone in the lobby of a public building, which is programmed to ring only the number of a telephone dispatcher. Nailing down a switched connection saves the cost of running a circuit between the two points. The resources in such a connection can be released when no longer needed, for example, a television circuit from a parade route back to the studio

8.
T-Mobile UK
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T-Mobile UK was a mobile network operator in the United Kingdom, owned by Deutsche Telekom since 1999, and originally launched as One2One. In 2009, Deutsche Telekom and Orange SA announced that the T-Mobile network was to be merged with Orange UK in a joint venture, EE withdrew the T-Mobile brand in February 2015. The network was launched as Mercury One2One, a GSM mobile network operated by the now-defunct Mercury Communications. It was the worlds first GSM1800 network when it was launched in September 1993, the network was purchased by Deutsche Telekom in 1999 and rebranded as T-Mobile in summer 2002. T-Mobile offered both pay-as-you-go and pay-monthly contract phones, the pay-monthly contracts consisted of set amounts of minutes and flexible boosters which allow the customer to change them month to month depending on their needs. Prior to this T-Mobile had an option known as Flext which gave the user an amount of money to use for calls, texts, MMS. This was withdrawn in early 2010, there is no warning when pay-monthly customers exceed their monthly inclusive limit, leading to unexpectedly large bills. T-Mobile launched their 3G UMTS services in the Autumn of 2003, on 12 December 2007, it was confirmed that a merger of the high-speed 3G and HSDPA networks operated by T-Mobile UK and 3 was to take place starting January 2008. This resulted in T-Mobile and 3 having the largest HSDPA mobile phone network in the country, with HSDPA access initially restricted to WebnWalk Plus customers, the long-term future of either brand was unclear, though EE stated that both would be retained for the first eighteen months at least. In 2013, parent company EE began to withdraw the T-Mobile brand, as of February 2015, T-Mobile connections are no longer possible to new or existing customers. On 11 May 2010 it was announced both the Orange and T-Mobile brands will remain on British high streets, although their new merged parent company will be called EE. As a result, there are around 700 EE stores open in the UK, as of February 2015, EE stores only offer EE products, with T-Mobile services withdrawn. T-Mobiles UK network was used as the backbone network behind Virgin Mobile UK. Post-merger, Virgin Mobile continues to run on the EE network, on March 26,2014, the T-Mobile UK website was closed and redirected to the EE website. In February 2015, T-Mobile UK and Orange UK tariffs were no longer offered to new or upgrading customers, existing T-Mobile UK and Orange UK plans continue to use EEs 2G and 3G networks. T-Mobile says, Browsing means looking at websites and checking email, UK Information Commissioner Christopher Graham said the data was sold for “substantial amounts of money” to brokers working for other mobile phone companies. The privacy watchdog said it planned to prosecute and would push for jail terms for anyone convicted, rival companies bought the information and used it to make cold calls to the customers offering them a new contract with a new network